PUBLISHED under R67 (condition T-B) — NOT house-adjudicated. Build S371a. What PUBLISHED means here (R72): two non-drafting AI lanes (gemini + grok) read this record's anchor citation on different objects and agreed it SUPPORTS the record's statement; no citation on the record is disputed as support; its machine certificate is current. What it does not mean: no person has signed off on this record (adjudication: NOT_ADJUDICATED), the drafting lane's own reads count for nothing, and 3 of 3 unblocked uses were REVIEWED — the rest were read by one lane or none. Every label shown is the label as printed in the suite of record (Rev33.1_S369 (PDF sha256 b64ddcd9e16a6dcd…)); no house tier is assigned. The state is recomputed from the uses on every build and is withdrawn if they stop justifying it. Receipt: condition R67-TB · anchor SU-af70cf9e0a954e10df55ed03 · master 3fb7fca1ceb9ba49 · S337.

LIB2-077 · The unitary matter-colour class has no image-compatible adjoint

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 10

Label sentence at the locator (PDF p.176 (bytes of record)):

dimension 140, matching the character prediction 140 = 2·15 (36⊕36)+2·55 (420⊕420) exactly (singular-value gap 8.9 × 1013 ). The union of the rowspaces of all invariant Θ has rank 125,

Statement

For the registered unitary matter-colour class, the invariant embedding-tensor space has dimension 140, and the union of its rowspaces has rank 125, its eight missing directions being exactly the su(3) adjoint.

Parts of the statement (4)

Each part is a clause of the statement above, cut so that one part makes one claim. A reader naming the clause a quote supports can name the part.

p1 · the invariant embedding-tensor space has dimension 140 (one claim)
p2 · the union of its rowspaces has rank 125, its eight missing directions being exactly the su(3) adjoint. (cut further below)
p2-p1 · the union of its rowspaces has rank 125 (one claim)
p2-p2 · its eight missing directions being exactly the su(3) adjoint (one claim)

Scope

carrier	Inv_su(3),unitary(912) and its combined rowspace in the 133
domain	Rowspace orthogonality to the required colour adjoint.
group	su(3)
hypotheses	The unitary class is 8 = 3 ⊕ 5·1.; Use the registered invariant embedding-tensor space and rowspace conventions.
quantifier	The specified invariant space for this embedding class.
real form	Compact unitary-class su(3) in su(8)

What this does not show. This embedding-class result does not identify a physical colour action elsewhere or supply a derivation of the compact Standard-Model boundary.

Scientific status: UNDER REVIEW — the house has not adjudicated CURRENT / CONTESTED for this record (charter §10.3); a drafted claim is a claim under review, not a result.

Sources in the suite of record

Key — use ≠ record. A review state printed on a source use below names that use — one citation of the suite, read by the lane named in its warrant — not this record. The record's own review state is the one in the table above and is unchanged by any use-level state; a use may be LANE_PROPOSED or REVIEWED while the record it sits on remains IN_REVIEW (R45, R49).

Quotes are verbatim from the sha-pinned text extraction of the Rev33.1 PDF (A1584 §2.2, S309): mathematical typography — radicals, exponents, ≅ — can appear displaced in the extracted line. The PDF page is authoritative; the quote is what the machine gate matched.

Appendix F, §3, Leg A: invariant-space dimension and rowspace rank — PDF p.182 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

dimension 140, matching the character prediction 140 = 2·15 (36⊕36)+2·55 (420⊕420) exactly (singular-value gap 8.9 × 1013 ). The union of the rowspaces of all invariant Θ has rank 125,

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_f_gauge_boundary.tex:191-195): dimension 140, matching the character prediction 140=2·15 (36⊕36̄) +2·55 (420⊕420̄) exactly (singular-value gap 8.9×10¹³). The union of the rowspaces of all invariant Θ has rank 125, (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix F, §3, Leg A: missing adjoint — PDF p.183 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

the eight missing directions are precisely the su(3) adjoint itself (full isotypic orthogonality).

Appendix F, §3, Unit-class representation content — PDF p.182 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

matter colour is the unitary class 8 = 3 ⊕ 5 · 1, with 56-content 20 · 1 ⊕ 6 · 3 ⊕ 6 · 3̄ and no octet.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	Appendix F §3, invariant-912 and rowspace checks, pp.176–177; A761h	—	unknown	The dimensions and adjoint exclusion are source-reported. The rowspace certificate and original replication output are not attached.

The numbers this record declares, and where each one's digits come from

This table covers the values this record DECLARES, not every numeral printed on this page: group labels such as E7(7), section numbers and page numbers are not declared values and are not listed here.

value as printed	page	digit source
`140`	PDF p.176 (bytes of record)	suite text p.176 only (no kernel line found)
`125`	PDF p.176 (bytes of record)	suite text p.176 only (no kernel line found)
`3`	PDF p.176 (bytes of record)	suite text p.176 only (no kernel line found)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-076 The enumerated compact embeddings fail the simultaneous-adjoint test	—

Why this record is PUBLISHED (R67, condition T-B)

states a predicate	yes
uses on the record · unblocked	3 · 3
uses any lane has read	3 of 3
REVIEWED SUPPORTS use on the predicate, read by two non-drafting lanes	yes (2)
a SUPPORTS use on the predicate is DISPUTED	no
machine certificate current	yes

Machine certificate (R68)

state MACHINE_CHECKS_PASSED

policy sgtoe-clearance-policy-1.0-RATIFIED · sha16 ef7d6e7690514311

bound to master aad7a3ec6ce3b510 (the master the checks ran on; issued 2026-09-26T05:06Z)

checks

check	result	reason
`schema_valid`	PASS	exercised
`basis_current`	PASS	exercised
`quote_located`	PASS	exercised
`labels_literal`	PASS	exercised
`edges_resolved`	PASS	exercised
`bindings_valid`	PASS	exercised

A certificate says the record is well-formed, current, quote-on-page, label-literal, edge-resolved and binding-consistent on the bytes it was issued on. It is not a review, and it goes STALE the moment the master moves under it (R68). It is one conjunct of the PUBLISHED condition (R67), never the whole of it.

History

March library (v1) antecedents	no legacy antecedent identified
Track-2 claim ids	B-CH-01 — cross-reference; the Track 1 / Track 2 join sets each one against what the sealed suite prints for this record. Where they differ, the suite is the record.
serials	A761h
candidate ids (frozen list S304)	C2-038

Drafting-lane note

C2-038 remains tied to the registered unitary class and its invariant space. It is distinct from the simultaneous colour-plus-weak branching test and does not import an unrun rowspace certificate.

Receipt

round D1253 · parsed 2026-09-06T00:06Z · machine gates passed: CONTRACT, G1-quote-on-page, G2-numerals-declared, G4-ids-resolve, DAG-acyclic · content sha256 b99eb22b4883307896b8e25a1799f9c3b86038bb8c1456719589fcb0c982ed95

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-077 | PASS or FAIL(G1–G8) or NOT RUN | quote | PDF page | one sentence. G1 source supports the exact scoped assertion · G2 evidence class fits (numbers ≡ digit source) · G3 labels as printed, not converted · G4 comparison typed · G6 public scope · G7 history real · G8 caution present and true. Machine surfaces: index.json · capsule.md.

Generated from library_v2.jsonl. Declared volatile fields (R36): BUILD_STAMP.
BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02